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hw1(2) - x 3 dx e x" 1 $ = 4 15 b Now do a similar...

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EE 439 — Fall 2009 HW problem 1 Name(s) __________________________________. Due: Oct. 7, 2009 Please put your answers on this sheet. Staple additional work behind. Be sure to include all your work. a. Starting with Planck’s expression for the energy density spectrum inside a black-body cavity "# ( ) = 8 $ h c 3 # 3 exp h kT % ( ) * + 1 , derive the Stefan-Boltzmann law for the total energy density in the black body " T = aT 4 where a = 7.56x10 –16 Jm –3 K –4 . (Potentially useful information:
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Unformatted text preview: x 3 dx e x " 1 # $ = % 4 15 .) b. Now, do a similar calculation to give an expression for the total energy density above a certain frequency, ν o , where ν o is high enough to assume that h ν o >> kT. In this case, the integral will have a lower limit of ν o . The integration becomes quite easy if you modify the spectrum expression as allowed by the condition on the frequency limit....
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